Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 5000.1-d over \(\Q(\sqrt{-2}) \)
Isogeny class 5000.1-d contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
5000.1-d1 | \( \bigl[0\) , \( -1\) , \( 0\) , \( -83\) , \( -88\bigr] \) |
5000.1-d2 | \( \bigl[a\) , \( 1\) , \( a\) , \( -176\) , \( -926\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)